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neco model questions vol1 2022 mathematics | Objective

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Question 1 View Details

A right circular cone is inscribed in a sphere of radius \(R = 10\) cm. The cone's height is twice its base radius. Find the volume of the cone in cubic centimeters, giving your answer in exact form.

A. \(\frac{2048}{3}\pi\) cm\(^3\)

Correct B. \(\frac{1024}{3}\pi\) cm\(^3\)

C. \(\frac{512}{3}\pi\) cm\(^3\)

D. \(\frac{1024}{9}\pi\) cm\(^3\)

Correct Answer: B

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Question 2 View Details

If the variable \(x\) satisfies \(x + \frac{4}{x} = 5\) and \(x > 2\), evaluate the expression \(E = \frac{x^{3} - 8}{x^{2} - 4x + 4}\).

A. 10

B. 12

C. 16

Correct D. 14

Correct Answer: D

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Question 3 View Details

In a cyclic quadrilateral \(ABCD\), the side lengths are \(AB = 5\) cm, \(BC = 8\) cm, \(CD = 7\) cm, and \(DA = 6\) cm. The angle \(\angle ABC\) measures \(120^{\circ}\). Find the length of diagonal \(BD\) in centimeters, expressed in simplest radical form.

Correct A. \(\frac{83}{\sqrt{129}}\) cm

B. \(\frac{83\sqrt{129}}{130}\) cm

C. \(\frac{85}{\sqrt{129}}\) cm

D. \(\frac{83}{\sqrt{130}}\) cm

Correct Answer: A

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Question 4 View Details

In triangle \(ABC\), point \(D\) lies on side \(BC\) such that \(BD:DC = 3:5\). A line through \(D\) parallel to side \(AB\) meets side \(AC\) at \(E\). If the area of triangle \(ADE\) is \(24\) cm\(^2\), determine the area of triangle \(ABC\) in square centimeters.

A. 108.8 cm\(^2\)

B. 112.5 cm\(^2\)

C. 96.0 cm\(^2\)

Correct D. 102.4 cm\(^2\)

Correct Answer: D

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Question 5 View Details

In the diagram, triangle \(ABC\) has \(\angle A = 40^{\circ}\), \(\angle B = 70^{\circ}\), \(\angle C = 70^{\circ}\) and side \(AB = 12\) cm. Point \(D\) lies on side \(BC\) with \(BD:DC = 1:2\). Find the length of segment \(AD\) in centimeters, correct to two decimal places.

A. 13.57 cm

Correct B. 11.36 cm

C. 9.81 cm

D. 10.24 cm

Correct Answer: B

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Question 6 View Details

In the coordinate plane, point A has coordinates \((1,2)\). Point B has coordinates \((5,k)\) where \(k\) is an integer. Point C is \((9,6)\). The line \(L\) passes through A and is perpendicular to the line through B and C. It is also known that \(L\) passes through the midpoint of segment BC. Find the value of \(k\) and give the equation of line \(L\) in the form \(y = mx + c\).

Correct A. k = 10; equation: y = x + 1

B. k = 8; equation: y = x + 3

C. k = 6; equation: y = -x + 7

D. k = 12; equation: y = 2x - 1

Correct Answer: A

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Question 7 View Details

A data set consists of the values 1, 3, 5, 7 and 9 with respective frequencies 3, 4, a, 2 and 1. The mean of the data set is 4.5. Find the missing frequency \(a\) and then determine the median of the data set.

A. a = 12; median = 6

B. a = 14; median = 4

C. a = 10; median = 5

Correct D. a = 14; median = 5

Correct Answer: D

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Question 8 View Details

A recipe requires \(2\frac{1}{3}\) cups of flour and \(\frac{3}{4}\) cup of sugar. If the chef wants to make four times the recipe, how many cups of flour and sugar together are needed? Express your answer as a mixed number.

A. 12\frac{2}{3} \text{ cups} \;(= \frac{38}{3} \text{ cups})

B. 13\frac{1}{3} \text{ cups} \;(= \frac{40}{3} \text{ cups})

Correct C. 12\frac{1}{3} \text{ cups} \;(= \frac{37}{3} \text{ cups})

D. 11\frac{1}{3} \text{ cups} \;(= \frac{34}{3} \text{ cups})

Correct Answer: C

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Question 9 View Details

An arithmetic sequence has general term \(a_n = 4n + k\). The sum of the first eight terms is 200. Find the constant \(k\) and then give the 12th term of the sequence.

A. k = 5; 12th term = 53

Correct B. k = 7; 12th term = 55

C. k = 9; 12th term = 59

D. k = 7; 12th term = 57

Correct Answer: B

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Question 10 View Details

In the plane, let \(\mathbf{u} = (3,\,k)\) and \(\mathbf{v} = (m,\,5)\). It is known that \(\mathbf{u} + \mathbf{v}\) is parallel to the vector \((1,2)\) and that the magnitude of \(\mathbf{u} - \mathbf{v}\) is 5. Find the ordered pair \((k,\,m)\) and then compute the area of the parallelogram formed by \(\mathbf{u}\) and \(\mathbf{v}\).

A. (k, m) = (2, -1); area = 12

B. (k, m) = (0, 1); area = 10

C. (k, m) = (-1, 2); area = 18

Correct D. (k, m) = (1, 0); area = 15

Correct Answer: D

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Question 11 View Details

The time (T) (in minutes) taken to fill a tank varies directly with the volume (V) (in litres) and inversely with the flow rate (r) (in litres per minute). When a 500‑L tank is filled at a flow rate of (25\ \text{L min}^{-1}\), it takes 20 minutes. The pump is then upgraded, increasing the flow rate by 20 %. Using the same constant of variation, how long will it now take to fill a 750‑L tank?

A. 20

B. 35

C. 30

Correct D. 25

Correct Answer: D

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Question 12 View Details

An urn contains 4 red, 5 blue and 3 green balls (total 12). Three balls are drawn sequentially without replacement. Given that exactly two of the three drawn balls are red, what is the probability that the first ball drawn was red?

A. 1/3

Correct B. 2/3

C. 1/2

D. 3/4

Correct Answer: B

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Question 13 View Details

The cost \(C\) (in naira) to produce \(x\) widgets varies directly as the square of the number of widgets and inversely as the number of workers \(w\) employed. When 200 widgets are produced by 5 workers, the cost is \(\text{₦}12\,000\). If the factory wants to produce 300 widgets using 6 workers, what will be the cost?

Correct A. 22500

B. 27000

C. 135000

D. 15000

Correct Answer: A

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Question 14 View Details

What is the least common multiple of 12 and 18?

A. 12

Correct B. 36

C. 54

D. 24

Correct Answer: B

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Question 15 View Details

There are two boxes. Box X contains 2 red and 3 blue balls. Box Y contains 4 red and 1 blue ball. A box is selected at random, then a ball is drawn at random, its colour noted, and the ball is replaced. The same box is used for a second draw. Both drawn balls are observed to be red. What is the probability that the selected box was Box Y?

Correct A. 4/5

B. 3/5

C. 2/5

D. 1/5

Correct Answer: A

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Question 16 View Details

Find the sum of all integer values of \(x\) that satisfy both inequalities \(\frac{x+2}{x-3} > 0\) and \(x^{2} - 7x + 6 \le 0\).

Correct A. 15

B. 20

C. 13

D. 16

Correct Answer: A

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Question 17 View Details

The quadratic equation \(x^{2}-(k+1)x+(k-2)=0\) has integer roots that differ by 3. Find the sum of all possible values of the parameter \(k\).

A. 5

Correct B. 2

C. 1

D. 3

Correct Answer: B

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Question 18 View Details

Simplify the expression \(E = \frac{3x^{2} - 12x + 12}{x^{2} - 4x + 3}\). If \(x\) satisfies \(x + \frac{1}{x} = 3\), the expression \(E\) can take two possible values. Find the sum of these possible values.

A. 2

Correct B. 3

C. 5

D. 4

Correct Answer: B

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Question 19 View Details

Solve the inequality \(|2x - 5| < x + 3\). Then, find the sum of all integer values of \(x\) that satisfy the inequality.

A. 24

B. 32

Correct C. 28

D. 30

Correct Answer: C

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Question 20 View Details

A sequence \(\{a_n\}\) is defined by \(a_{1}=k\) and the recurrence relation \(a_{n+1}=3a_{n}-2\) for \(n\ge 1\). If the sum of the first five terms is 242, determine the value of the sixth term \(a_{6}\). Express your answer as an irreducible fraction.

A. 19318/121

Correct B. 57712/121

C. 57470/121

D. 57591/121

Correct Answer: B

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Question 21 View Details

In the coordinate plane the points are A(2,5), B(12, -1) and C(-4,7). Point P divides AB internally in the ratio AP:PB = 2:3. Find the coordinates of P, then determine the equation of the line through P and C, and finally give the x‑intercept of that line. Express the x‑intercept as a fraction in lowest terms.

A. 131/12

B. 140/11

Correct C. 131/11

D. 123/11

Correct Answer: C

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Question 22 View Details

A quadratic function passes through the points \((0,2)\), \((2,10)\) and \((4,26)\). Assuming the function is of the form \(y = ax^{2}+bx+c\), determine the exact expression for \(y\) in terms of \(x\).

A. y = x^{2} + 3x + 2

B. y = x^{2} - 2x + 2

C. y = x^{2} + 2x + 1

Correct D. y = x^{2} + 2x + 2

Correct Answer: D

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Question 23 View Details

The time \(t\) (in seconds) taken for a particle to travel a distance \(s\) (in metres) under a constant force \(F\) (in newtons) varies directly as \(s\) and inversely as \(\sqrt{F}\). If it takes 8 s to travel 20 m when the force is 4 N, how many seconds will it take to travel 45 m when the force is 9 N?

A. 9

B. 14

Correct C. 12

D. 10

Correct Answer: C

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Question 24 View Details

In triangle \(ABC\) we have \(AB = 7\) cm, \(AC = 9\) cm and \(\angle BAC = 45^{\circ}\). Point \(D\) lies on side \(BC\) such that \(BD = 4\) cm. Find the length of \(AD\) (give your answer to two decimal places).

A. 6.85

Correct B. 7.71

C. 9.13

D. 8.20

Correct Answer: B

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Question 25 View Details

A school sells tickets for a concert. Adult tickets cost \(\,\)₦1500 each and student tickets cost \(\,\)₦800 each. On a particular day the total revenue was \(\,\)₦129,000 and exactly 100 tickets were sold. The number of adult tickets sold was ten more than twice the number of student tickets sold. How many adult tickets were sold?

A. 60

Correct B. 70

C. 55

D. 80

Correct Answer: B

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